What is the derivative of $log(sin^2(x))$ ?

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Answer 1 · 2015-08-31T18:53:27

If you don't remember the derivative of $log_10(u)$ , you can derive it like so:

$y = log(sin^2x)$
$10^y = sin^2x$

$d/(dx)[10^y] = 10^yln10((dy)/(dx))$

(It is an extension of $d/(dx)[a^x] = a^xlna$ .)

Therefore, you get:

$10^yln10((dy)/(dx)) = 2sinxcosx$

$color(blue)((dy)/(dx)) = (2sinxcosx)/(10^yln10)$

$= (2sinxcosx)/(sin^2x*ln10)$

$color(blue)(= (2cotx)/(ln10))$

What is the derivative of log(sin^2(x))log(sin^2(x))?